\(\bullet \)  Tighter Regret Bounds. To the best of our knowledge, there is a gap in the regret bounds of contextual linear bandits: the state-of-the-art lower bounds are, \(\Omega (d\sqrt{T})\)  for linear bandits [1]} and \(\Omega (d\sqrt{T\log T})\)  for linear contextual bandit with adversarial contexts [2]}.
